Homological algebra
Identifieur interne : 002246 ( Main/Exploration ); précédent : 002245; suivant : 002247Homological algebra
Auteurs : Masaki Kashiwara [Japon] ; Pierre Schapira [France]Source :
- Grundlehren der mathematischen Wissenschaften [ 0072-7830 ] ; 1990.
Abstract
Summary: This chapter contains the bases of homological algebra which are necessary for the understanding of the rest of this book: categories and functors, triangulated categories, localization, derived categories, ind-objects and pro-objects, Mittag-Leffler condition. Since it is not possible to present in a single chapter the whole theory with all details, we have left out as an exercise some auxiliary results and we have postponed to Chapter X the theory of t-structures, which is not used until there. Of course, the reader will also consult with great benefit the (classical) books and papers on this subject, such as Bourbaki [1], Cartan-Eilenberg [1], Freyd [1], Gabriel-Zisman [1], Godement [1], Grothendieck [1], Hilton-Stammbach [1], Iversen [1], MacLane [1], Mitchell [1], Northcott [1], and expecially Deligne [1], Gelfand-Manin [1], Hartshorne [1] and Verdier [2] concerning derived categories.
Url:
DOI: 10.1007/978-3-662-02661-8_3
Affiliations:
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